Motion along a line

Strange to think but a very common idea in physics is the idea of a particle. A point like concentration of matter that has no size, no shape, and no internal structure: A singularity! 🙂

The branch of physics concerned with the description of motion is known as Kinematics. It is not concerned with forces, nor with the causes of motion.

Its concerns are:

Where is the particle

How fast is it moving and in what direction.

How rapidly is it speeding up or slowing down

Easiest to describe with a graph of Position against time: e.g. For:

Time/t

Position/m

1

1

2

4

3

9

4

16

5

25

(Yes, I know the graph doesn’t have any labels and it really should, but have you ever tried using Word to create a graph!?) Anyway. . . Position/m along the vertical axis, and Time/s along the horizontal. (Even worse… You ever tried copying a Word graph to HTML and a Blog!!?)

The above graph represents the position of a particle whose velocity is changing with time, it’s speeding up, accelerating. If the speed was constant you’d see the graph below

Time/t

Position/m

1

2

2

4

3

6

4

8

5

10

Again: Position/m along the vertical axis, and Time/s along the horizontal.

This constant speed is known as Uniform Motion and as you can see it creates a straight line graph.

The general form of equation for a straight line is:

S=At + B, where A and B are constants. B being the intercept (where the sloping line crosses the vertical axis) and A being the slope (the steepness of the line), t is the value along the vertical axis (which in this case is time/t).

Velocity is defined as the rate of change of position with respect to time, i.e.

(change of position)/(change in time) = (x2-x1)/(t2-t1), sometimes referred to as the ‘rise over the run’

Speed and velocity are not the same. Velocity has a direction whereas speed is just a value. It is the magnitude of the velocity, i.e, the value of the velocity irrespective of its sign (or direction), often written as |v|

In graphical terms, the velocity Δs/Δt is the slope of the particle’s position-time graph, the steepness of line representing the particles speed.

The initial position of the particle (i.e. where it was at time, t = 0), is where the line crosses the vertical axis, known as the intercept.

From the equation of a straight line graph it is easy to see that the Uniform Motion Equation is: